Editorial Type:
Article
Article Type:
Research Article

Uniform Asymptotics for the Linear Kelvin Wave in Spherical Geometry

John P. Boyd University of Michigan, Ann Arbor, Michigan

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Cheng Zhou University of Michigan, Ann Arbor, Michigan

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Print Publication:
01 Feb 2008
DOI:
https://doi.org/10.1175/2007JAS2356.1
Page(s):
655–660
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Abstract

The Kelvin wave is the gravest eigenmode of Laplace’s tidal equation. It is widely observed in both the ocean and the atmosphere. In the absence of mean currents, the Kelvin wave depends on two parameters: the zonal wavenumber s (always an integer) and Lamb’s parameter ϵ. An asymptotic approximation valid in the limit s2 + ϵ ≫ 1 is derived that generalizes the usual “equatorial wave” limit that ϵ → ∞ for fixed s. Just as shown for Rossby waves two decades ago, the width of the Kelvin wave is (ϵ + s2)−1/4 rather than ϵ−1/4 as in the classical equatorial beta-plane approximation.

Corresponding author address: John Boyd, University of Michigan, 2455 Hayward Ave., Ann Arbor, MI 48109-2143. Email: jboyd@umich.edu

Abstract

The Kelvin wave is the gravest eigenmode of Laplace’s tidal equation. It is widely observed in both the ocean and the atmosphere. In the absence of mean currents, the Kelvin wave depends on two parameters: the zonal wavenumber s (always an integer) and Lamb’s parameter ϵ. An asymptotic approximation valid in the limit s2 + ϵ ≫ 1 is derived that generalizes the usual “equatorial wave” limit that ϵ → ∞ for fixed s. Just as shown for Rossby waves two decades ago, the width of the Kelvin wave is (ϵ + s2)−1/4 rather than ϵ−1/4 as in the classical equatorial beta-plane approximation.

Corresponding author address: John Boyd, University of Michigan, 2455 Hayward Ave., Ann Arbor, MI 48109-2143. Email: jboyd@umich.edu

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